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Now You See It

The modulation transfer function describes the contrast and resolution of an optical component, and is one key to determining image quality.

In order for an optical imaging system to be successful, it must provide images of sufficient quality. Exactly what qualifies as sufficient quality depends on the application, but is always a combination of resolution and contrast, as well as distortion and perspective errors. In this article, we will take a close look at the first two factors.

Resolution is a measure of an imaging system's ability to reproduce object detail. A low-resolution image contains blurry scenes in which objects lack detail. A high-resolution image provides crisp edges and includes much detail.

Contrast also factors into image quality because it expresses how well an image differentiates between an object's shades of gray. An image with low contrast will appear washed out because it lacks vivid blacks and whites.

Resolution and contrast are closely related. Think of imaging a target with alternating equal width black and white lines, also called a line-pair (Figure 1a). This target represents 100% contrast. No lens--not even a perfect one--at any resolution can fully transfer this contrast information to the image. The diffraction limit, dictated by physics, limits the ability to transfer information.

Now imagine that the width of the line pairs on the target decreases. In other words, the frequency of the line pairs, measured in line pairs per millimeter (lp/mm), increases. As frequency increases, the lens is less able to transfer the contrast, so the resulting image has less contrast.

What's MTF?
The components of the imaging system have a standard specification that describes both resolution and contrast: the Modulation Transfer Function (MTF). MTF describes the component's ability to transfer contrast at a particular resolution, or frequency, from an object to an image. In other words, the MTF indicates how much of the object's original contrast gets lost as the frequency in the object being imaged increases.

An MTF graph for a component plots the percentage of transferred contrast vs. the frequency of the lines. As mentioned, the contrast in the image decreases with increased frequency. The MTF illustrated in Figure 2 was measured both on axis (at the center of the image) and for the full field (toward the corner edges of the field or off axis). These measurements tell how well the lens can resolve features throughout a field of view. Notice that the plot includes both horizontal and vertical performance. The difference between these two measurements indicates the amount of astigmatism present in the image.

Combine 'em
The usual rule-of-thumb technique for predicting a system's performance suggests that the system's resolution depends mainly on the component with the lowest resolution. While this is useful for quick estimates, it can be misleading. In fact, systems tend to have lower resolution than predicted by this rule because all of the optical and electronic system components reduce resolution to some extent. These estimates also fail to consider contrast, another aspect critical to image quality.

To accurately predict the image quality of the optical system, combine the effects of each component to determine how the overall system will affect resolution and contrast. Within a system, every component--such as the lens, camera, cables and capture board--has an MTF. To accurately determine whether a particular lens provides sufficient image quality, multiply its MTF function by the MTF function for each component in the system. The system MTF is the product of all of the component MTF curves.

For example, suppose your system consists of a lens mounted on a Sony XC-ST50 CCD monochrome camera. Consider the two lenses described in Figure 2: a 25-millimeter fixed focal-length lens and a 25-millimeter MVO Double-Gauss lens. Analyze the lens-camera MTF curves for each combination, and consider what contrast is needed at what resolutions. If a minimum contrast of 35% for an image resolution of 30 lp/mm is needed, then the MVO Double-Gauss lens is the better choice.

Be aware
A theoretical MTF plot is often supplied by the manufacturer for a specific lens. You may want to make sure that the plot is realistic. Manufacturing always introduces some imperfections that degrade the performance of a lens. Accurate MTFs can be obtained either from software, as long as it takes the manufacturing tolerances into consideration, or by measuring the actual MTF of the lens after manufacturing, which provides more accurate values. Be sure to ask for measured MTF data when you're-evaluating lenses for machine vision systems.

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